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JOINT COMMUNICATION AND SENSING OVER STATE DEPENDENT
CHANNELS
by
Chiranjib Choudhuri
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(ELECTRICAL ENGINEERING)
May 2013
Copyright 2013 Chiranjib Choudhuri

The fundamental trade-off between communication rate and estimation error in sensing the channel state at the decoder is investigated for a discrete memoryless channel with discrete memoryless action dependent state when the state information is available either partially or fully at the encoder. We first investigate the capacity a relay channel with finite memory, where the action independent fixed channel state information is assumed to be known at both the encoder and decoder and then went on to investigate the problem of determining the trade-off between capacity and distortion for the channel with states known only at the encoder. ❧ The relay channel with finite memory is modeled with channels with inter-symbol interference (ISI) and additive colored Gaussian noise. The channel state or channel impulse responses are assumed to be known at both the encoders and decoder. Prior results are used to show that the capacity of this channel can be computed by examining the circular degraded relay channel in the limit of infinite block length. The thesis provides single letter expressions for the achievable rates with decode-and-forward (DF) and compress-and-forward (CF) processing employed at the relay. Additionally, the cut-set bound for the relay channel is generalized for the ISI/colored Gaussian noise scenario. All results hinge on showing the optimality of the decomposition of the relay channel with ISI/colored Gaussian noise into an equivalent collection of coupled parallel, scalar, memoryless relay channels. The region of optimality of the DF and CF achievable rates is also discussed. The resulting rates are illustrated through the computation of numerical examples. ❧ The problem of state communication over a discrete memoryless channel with discrete memoryless state when the state information is available strictly causally at the encoder is then studied. It is shown that block Markov encoding, in which the encoder communicates a description of the state sequence in the previous block by incorporating side information about the state sequence at the decoder, yields the minimum state estimation error. When the same channel is used to send additional independent information at the expense of a higher channel state estimation error, the optimal tradeoff between the rate of the independent information and the state estimation error is characterized via the capacity–distortion function. It is shown that any optimal tradeoff pair can be achieved via rate-splitting. These coding theorems are then extended optimally to the case of causal channel state information at the encoder using the Shannon strategy. ❧ For non-causal channel state knowledge at the encoder, information-theoretic lower and upper bounds (based respectively on ideas from hybrid-coding and rate–distortion theory) are derived on the capacity– distortion function. Some examples are provided, for which the capacity–distortion functions are characterized by showing that the two bounds match. These coding theorems are then extended to the case of source coding with side information vending machine at the encoder (introduced in [H. Asnani, H. Permuter, and T. Weissman. Probing capacity. IEEE Trans. Inf. Theory, 57:7317-7332, 2011.5]) to provide an improved lower bound on the rate–distortion function. In some of the communication scenarios, however, the decoder is not interested in estimating the state directly, but it wants to reconstruct a function of the state with maximum fidelity. This problem of modified state estimation over a discrete memoryless implicit channels (DMIC) with discrete memoryless (DM) states is studied when the state information is available non-causally at the encoder. Lower and upper bounds on the optimal distortion in estimating the input of the implicit channel are derived. The methods developed for the DMIC with DM state model are then used to investigate the optimal distortion for the asymptotic version of the Witsenhausen counterexample, one of the fundamental problems in distributed control theory. The minimum distortion is characterized for the counterexample; furthermore it is shown that the combination of linear coding and dirty-paper coding (DPC) proposed in [P. Grover and A. Sahai. Witsenhausen’s counterexample as assisted interference suppression. Special Issue on “Information Processing and Decision Making in Distributed Control Systems” of the International Journal of Systems, Control and Communications, 2010], in fact, achieves the minimum distortion for the Gaussian case when the proper amplification factor is determined. ❧ The results obtained with discrete memoryless state dependent channels are then extended to channels with action-dependent states, as defined in [T. Weissman. Capacity of channels with action-dependent states. IEEE Trans. Inf. Theory,56:5396-5411, 2010]. While [T. Weissman. Capacity of channels with action-dependent states. IEEE Trans. Inf. Theory,56:5396-5411, 2010] investigated the scenario of message dependent nonadaptive action sequences, this work focuses on characterizing the benefits of allowing adaptive action sequences, where the action is not only a function of the message, but it also depends strictly causally on the past observed state sequences. To compare the two framework, the problem of joint communication and state estimation is considered over an action dependent channel. The capacity–distortion tradeoff of such a channel is characterized for the case when the state information is available strictly causally/causally at the channel encoder. It has been shown that although adaptive action is not useful in increasing the unconstrained capacity of the channel, but it helps in achieving a better capacity–distortion function by decreasing the state estimation error at the decoder. Since the capacity–distortion function is open with non-causal channel state information at the encoder, the capacity of such a channel is characterized and it is shown that the adaptive action is not useful in increasing the capacity. The result is illustrated with an example of action dependent additive Gaussian channel, whose capacity is characterized by showing the equivalence of the current setting to the problem of the cooperative multiple access channel (MAC) with asymmetric state information at the encoders [A. Zaidi, P. Piantanida, and S. Shamai. Multiple access channel with states known noncausally at one encoder and only strictly causally at the other encoder. In Proc. IEEE Int. Symp. Inf. Theory, St Petersburg, Russia, 2011]. ❧ To illustrate the results of state communication with a practical example, the problem of planning the trajectory of a robotic vehicle to gather data from a deployment of stationary sensors is studied. The purpose of collecting data from the sensors is to monitor a source signal present in the environment. Here the source signal is the state of the system, which affects the communication channel between the sensors and the autonomous vehicle. The robotic vehicle and the sensors are equipped with wireless modems (e.g., radio in terrestrial environments or acoustic in underwater environments), which provide noisy communication across limited distances. In such scenarios, the robotic vehicle can improve its efficiency by planning an informed data gathering trajectory. Prior work has proposed information theoretic performance metrics for these problems based on mutual information and Fisher information, but such metrics do not properly account for stochastic variations in the quantity being measured and also they don’t explicitly provide a reconstructed source signal, which is one of the main objective of monitoring an unknown source signal. A novel performance metric for data gathering in robotic sensor networks based on the concept of squared error distortion is proposed. This metric provides a principled approach for modeling source variations and communication limitations during data collection. The formal properties of the distortion function is analyzed, and the squared error distortion with correlated sources, sources with unknown location and sources with unknown kinematics is determined using our results on state communication over state dependent channels. A sampling-based motion planning algorithm for optimizing data gathering tours for minimal distortion is also proposed and the proposed algorithms is compared in simulation, to show that distortion metrics provide significant improvements in data gathering efficiency. ❧ Lastly, The problem setting is extended to study the rate–distortion region of some distributed source coding problems, where action dependent side information “vending machine” is available to some of the decoders. These source coding problems can be thought of as a source coding dual of the channel coding problems with action dependent side information at the encoders. The model of a side information “vending machine” (VM) accounts for scenarios in which the measurement of side information sequences can be controlled via the selection of cost-constrained actions. In this thesis, the three-node cascade source coding problem is studied under the assumption that a side information VM is available and the intermediate and/or at the end node of the cascade. A single-letter characterization of the achievable trade-off among the transmission rates, the distortions in the reconstructions at the intermediate and at the end node, and the cost for acquiring the side information is derived for a number of relevant special cases. It is shown that a joint design of the description of the source and of the control signals used to guide the selection of the actions at downstream nodes is generally necessary for an efficient use of the available communication links. In particular, for all the considered models, layered coding strategies prove to be optimal, whereby the base layer fulfills two network objectives: determining the actions of downstream nodes and simultaneously providing a coarse description of the source. Design of the optimal coding strategy is shown via examples to depend on both the network topology and the action costs. Examples also illustrate the involved performance trade-offs across the network.

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JOINT COMMUNICATION AND SENSING OVER STATE DEPENDENT
CHANNELS
by
Chiranjib Choudhuri
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(ELECTRICAL ENGINEERING)
May 2013
Copyright 2013 Chiranjib Choudhuri